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Answer :
Final answer:
To find the right model for the wrestler's weight loss, the inequality must represent a weight greater than 165 and at most 185 after w weeks. The correct inequality for this scenario is option B: 165 < 189 - 0.5w ≤ 185.
Explanation:
The question asks which model represents the number of weeks, w, the wrestler needs to lose weight in order to be within the qualifying weight range for his class. Since the wrestler needs to weigh more than 165 pounds but less than or equal to 185 pounds, and he currently weighs 189 pounds losing 0.5 pounds per week, the correct inequality should allow for the wrestler's weight after w weeks to be greater than 165 pounds and at most 185 pounds.
The correct model is: B. 165 < 189 - 0.5w ≤ 185.
This inequality indicates that after w weeks of losing weight, the wrestler's weight must be more than 165 pounds and less than or equal to 185 pounds, which is exactly the requirement for the weight class.
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Answer:
B. [tex]165<189-0.5w\leq 185[/tex]
Step-by-step explanation:
Let w represent the number of weeks.
We have been given that a wrestler currently weighs 189 pounds and is losing 0.5 of a pound per week. So the weight lost by wrestler in w weeks would be [tex]0.5w[/tex].
The total weight of wrestler after w weeks would be:
[tex]189-0.5w[/tex]
We are also told that the wrestler needs to weigh more than 165 pounds but less than or equal to 185 pounds. This means that total weight of wrestler should be less than or equal to 185 pounds and greater than 165 pounds.
We can represent this information in an inequality as:
[tex]165<189-0.5w\leq 185[/tex]
Therefore, option B is the correct choice.
